What was already known
Strong target-preserving diffeomorphic approximation was known in the plane for all p≥1. The three-dimensional Ball–Evans problem remained open in the low-exponent range addressed here.
AI involvement
OpenAI credits itself as manuscript author and states that its internal frontier model produced the results in this release. Individual human input is not detailed enough to establish task-only autonomy.
OpenAI is named as author on the manuscript, and its release attributes the results to an internal frontier model. The individual human input is not detailed enough to establish autonomy.
Importance
Resolves the three-dimensional Ball–Evans approximation problem for 1≤p≤2.
Limitations
No smooth boundary, boundary extension, inverse Sobolev regularity or nonvanishing Jacobian is assumed; the original target domain is preserved.
Technical verification
Reported is the default when evidence for a higher level is insufficient. The OpenAI-authored manuscript reports and argues the result, but the reviewed sources do not document a completed check of the full assessed claim.
Human understanding
Few is the default when evidence for a higher level is insufficient. No named person is documented as explaining the central argument for this assessed contribution.
Correction and publication history
Primary manuscript, attribution, and prior-work review for non-notifying local inclusion; technical verification remains Reported.
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